{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:TPUJAOHVPZOXXHBUJSI6V2DS5K","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e98ec9d1e184d0d886aab8ec63db0e3b791eb1c55af0af3930a1e6568330c10f","cross_cats_sorted":["math.DS","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2019-07-09T20:20:06Z","title_canon_sha256":"5c2977d4262c5651fc54007588d4651623b52cae024b378dee5163a300519bf2"},"schema_version":"1.0","source":{"id":"1907.04392","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.04392","created_at":"2026-05-17T23:41:01Z"},{"alias_kind":"arxiv_version","alias_value":"1907.04392v1","created_at":"2026-05-17T23:41:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.04392","created_at":"2026-05-17T23:41:01Z"},{"alias_kind":"pith_short_12","alias_value":"TPUJAOHVPZOX","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"TPUJAOHVPZOXXHBU","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"TPUJAOHV","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:8e52f3783586837ff890b8f5b076c27835162e79a8b26b37ff74e585559c3991","target":"graph","created_at":"2026-05-17T23:41:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Gradient descent is arguably one of the most popular online optimization methods with a wide array of applications. However, the standard implementation where agents simultaneously update their strategies yields several undesirable properties; strategies diverge away from equilibrium and regret grows over time. In this paper, we eliminate these negative properties by introducing a different implementation to obtain finite regret via arbitrary fixed step-size. We obtain this surprising property by having agents take turns when updating their strategies. In this setting, we show that an agent th","authors_text":"Gauthier Gidel, Georgios Piliouras, James P. Bailey","cross_cats":["math.DS","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2019-07-09T20:20:06Z","title":"Finite Regret and Cycles with Fixed Step-Size via Alternating Gradient Descent-Ascent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.04392","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:516f515589b60abff22042af79976fc1aff4483cf998db59b3c1a98a455d01c9","target":"record","created_at":"2026-05-17T23:41:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e98ec9d1e184d0d886aab8ec63db0e3b791eb1c55af0af3930a1e6568330c10f","cross_cats_sorted":["math.DS","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2019-07-09T20:20:06Z","title_canon_sha256":"5c2977d4262c5651fc54007588d4651623b52cae024b378dee5163a300519bf2"},"schema_version":"1.0","source":{"id":"1907.04392","kind":"arxiv","version":1}},"canonical_sha256":"9be89038f57e5d7b9c344c91eae872eab2d38b355e7ea0a4018ea21de7d33f69","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9be89038f57e5d7b9c344c91eae872eab2d38b355e7ea0a4018ea21de7d33f69","first_computed_at":"2026-05-17T23:41:01.884154Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:01.884154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CL7Nr0aC/bJei9cqIpeYe9ZUgAZ/R/qeskvcIRXVUhCQJxjLyuLZ96sgG2DGpv/W6/ApdNXS2dce3D3oecgUBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:01.884835Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.04392","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:516f515589b60abff22042af79976fc1aff4483cf998db59b3c1a98a455d01c9","sha256:8e52f3783586837ff890b8f5b076c27835162e79a8b26b37ff74e585559c3991"],"state_sha256":"b22fa70dc40b9ff57cbfa235b50a8dbc36396b7925e6d3d46a030d69b0d0e2d4"}